Coulomb explosion and steadiness of high-radioactive silicate glasses
The paper is devoted to the theoretical study of Coulomb explosion in silicate glasses with low ionization potential under internal alpha-irradiation. The phenomenon was studied in the way of computer simulation, namely by the molecular dynamics (MD) method; parameters of the so-called lavalike...
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irk-123456789-1190182017-06-04T03:04:30Z Coulomb explosion and steadiness of high-radioactive silicate glasses Zhydkov, V. The paper is devoted to the theoretical study of Coulomb explosion in silicate glasses with low ionization potential under internal alpha-irradiation. The phenomenon was studied in the way of computer simulation, namely by the molecular dynamics (MD) method; parameters of the so-called lavalike fuel-containing materials (LFCM), were chosen as input parameters for the model due to its practical importance. LFCM are high-radioactive glasses, which were formed during an active stage of a well known heavy nuclear accident, occurred on Chornobyl NPP in 1986. Computer simulation revealed that Coulomb explosion really may occur in the LFCMs and leads to additional radiation damages under internal alpha-irradiation. The total quantity of atomic displacements produced in the way of Coulomb explosion from each alpha-particle track is 40000 to 80000, which exceeds radiation damages from alpha-particle and heavy recoil nuclei altogether (about 3500) more than one order. Ця робота присвячена теоретичному вивченню кулонівського вибуху в силікатних стеклах, що мають низький потенціал іонізації та перебувають під дією внутрішнього альфа-опромінення. Це явище було вивчено за допомогою комп’ютерного моделювання, а саме методом молекулярної динаміки (МД); параметри так званих лавоподібних паливомісних матеріалів (ЛПВМ), зважаючи на їх практичну значущість, були вибрані за вхідні параметри для цієї моделі. ЛПВМ – високорадіоактивні стекла, які утворилися впродовж активної стадії добре відомої важкої ядерної аварії, що відбулася на Чорнобильській АЕС в 1986. Комп’ютерне моделювання виявило, що кулонівський вибух дійсно може мати місце в ЛПВМ і призводить до додаткових радіаційних ушкоджень під дією внутрішнього альфа-опромінення. Загальна кількість атомних зміщень, утворених шляхом кулонівського вибуху від однієї альфа-частки, складає 40000 ÷ 80000, що більше за радіаційні пошкодження від альфа-частки і важкого ядра віддачі, взяті разом (близько 3500) більше, ніж на порядок. 2004 Article Coulomb explosion and steadiness of high-radioactive silicate glasses / V. Zhydkov // Condensed Matter Physics. — 2004. — Т. 7, № 4(40). — С. 845–858. — Бібліогр.: 23 назв. — англ. 1607-324X DOI:10.5488/CMP.7.4.845 PACS: 34.50.Fa, 34.90.+q, 72.90.+y http://dspace.nbuv.gov.ua/handle/123456789/119018 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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English |
| description |
The paper is devoted to the theoretical study of Coulomb explosion in silicate
glasses with low ionization potential under internal alpha-irradiation.
The phenomenon was studied in the way of computer simulation, namely
by the molecular dynamics (MD) method; parameters of the so-called lavalike
fuel-containing materials (LFCM), were chosen as input parameters
for the model due to its practical importance. LFCM are high-radioactive
glasses, which were formed during an active stage of a well known heavy
nuclear accident, occurred on Chornobyl NPP in 1986. Computer simulation
revealed that Coulomb explosion really may occur in the LFCMs and
leads to additional radiation damages under internal alpha-irradiation. The
total quantity of atomic displacements produced in the way of Coulomb explosion
from each alpha-particle track is 40000 to 80000, which exceeds
radiation damages from alpha-particle and heavy recoil nuclei altogether
(about 3500) more than one order. |
| format |
Article |
| author |
Zhydkov, V. |
| spellingShingle |
Zhydkov, V. Coulomb explosion and steadiness of high-radioactive silicate glasses Condensed Matter Physics |
| author_facet |
Zhydkov, V. |
| author_sort |
Zhydkov, V. |
| title |
Coulomb explosion and steadiness of high-radioactive silicate glasses |
| title_short |
Coulomb explosion and steadiness of high-radioactive silicate glasses |
| title_full |
Coulomb explosion and steadiness of high-radioactive silicate glasses |
| title_fullStr |
Coulomb explosion and steadiness of high-radioactive silicate glasses |
| title_full_unstemmed |
Coulomb explosion and steadiness of high-radioactive silicate glasses |
| title_sort |
coulomb explosion and steadiness of high-radioactive silicate glasses |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119018 |
| citation_txt |
Coulomb explosion and steadiness of high-radioactive silicate glasses / V. Zhydkov // Condensed Matter Physics. — 2004. — Т. 7, № 4(40). — С. 845–858. — Бібліогр.: 23 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT zhydkovv coulombexplosionandsteadinessofhighradioactivesilicateglasses |
| first_indexed |
2025-07-08T15:05:54Z |
| last_indexed |
2025-07-08T15:05:54Z |
| _version_ |
1837091684845879296 |
| fulltext |
Condensed Matter Physics, 2004, Vol. 7, No. 4(40), pp. 845–858
Coulomb explosion and steadiness of
high-radioactive silicate glasses
V.Zhydkov
Institute for NPP Safety Problems
of the National Academy of Sciences of Ukraine,
Kirova 36A, 07270, Chornobyl, Ukraine
Received August 16, 2004, in final form August 20, 2004
The paper is devoted to the theoretical study of Coulomb explosion in sili-
cate glasses with low ionization potential under internal alpha-irradiation.
The phenomenon was studied in the way of computer simulation, namely
by the molecular dynamics (MD) method; parameters of the so-called lava-
like fuel-containing materials (LFCM), were chosen as input parameters
for the model due to its practical importance. LFCM are high-radioactive
glasses, which were formed during an active stage of a well known heavy
nuclear accident, occurred on Chornobyl NPP in 1986. Computer simula-
tion revealed that Coulomb explosion really may occur in the LFCMs and
leads to additional radiation damages under internal alpha-irradiation. The
total quantity of atomic displacements produced in the way of Coulomb ex-
plosion from each alpha-particle track is 40000 to 80000, which exceeds
radiation damages from alpha-particle and heavy recoil nuclei altogether
(about 3500) more than one order.
Key words: Coulomb explosion, molecular dynamics, radioactive glasses
PACS: 34.50.Fa, 34.90.+q, 72.90.+y
1. Introduction
Coulomb explosion is the phenomenon of rapid spreading of positively charged
ions in condensed matter as a result of coulomb repulsion when high-density ionizati-
on of ensemble of neighbouring atoms takes place. This process has a threshold-like
dependence on ionization density, and when the energy of coulomb repulsion for
ensemble of ions surpasses the chemical bound energy, the process will develop in
explosion-like way, that is why this phenomenon is named a Coulomb explosion.
For the first time the phenomenon was detected in ionic crystals and solid rare
gases, where electrostatic interaction dominates over all other types of chemical
bonds [1].
Coulomb explosion generally requires the formation of high-density cluster of
positively charged ions much faster than charge relaxation time for current media.
c© V.Zhydkov 845
V.Zhydkov
Typical size of such a cluster is about 1 nm and typical time for this process is
200 fs. Due to a relatively long duration necessary to transform a potential ener-
gy into a kinetic energy the phenomenon occurs almost exclusively in dielectrics
and semiconductors, where ionic cluster cannot dissipate fast enough due to low
conductivity.
The formation of ion cluster sufficient for the Coulomb explosion can be provided
by intensive and short-time ionization energy pulses, which can be delivered to the
matter by means of a strong laser pulse [2] or high-energy charged particle [3].
The Coulomb explosion effects many phenomena; the most significant of them are
the surface sputtering and radiation damages. The Coulomb explosion in solids can
lead to a surface sputtering, defects, and clusters of defect formation. The Coulomb
explosion occurring as a result of charged particle flight leads to giant sputtering
yield value [4,5] and to a large amount of radiation damages [2,6], mainly atom-
ic displacements, which vastly increases DPA (Displacements Per Atom) value in
comparison to traditional collision model.
Each Coulomb explosion act produces a significant number of displaced atoms
[2]. Those atomic displacements are rather close-placed and form a large cluster of
radiation defects. This type of defects generally does not provide a visible effect on
macroscopic parameters of materials to a great extent, but rather serves as cracked
nuclei, which can significantly reduce their macroscopic mechanical steadiness if a
great number of such microcracks are formed. Such a cluster may dissolve in the
material volume with time, but high density of defects usually prevents this. Such a
process significantly increases a DPA quantity and leads to degradation of materials
undergoing self-irradiation due to internal agents.
An energy necessary for Coulomb explosion will be partially spent on ionization,
so the increase of ionization potential leads to a further increase of energy density
threshold. The high ionization energy is the main reason why Coulomb explosion
normally does not occur in pure quartz glass, except for the case of heavy multi-
charged ions [3], which can provide a large amount of potential energy. In glasses
having low ionization energy for electrons, however, the phenomenon may be sig-
nificant. Practical importance of glassy compositions, where an electron transport
dominates, stimulates the proposed design-theoretical study of Coulomb explosion
process for this type of materials.
First of all, one may notice, that Coulomb explosion effect is very hard to cal-
culate in analytical way. It needs taking into consideration a lot of factors, the
majority of which are significantly non-linear (potential, charge distribution). The
most convenient statistical and thermodynamic methods are generally unacceptable
here because the system is far from equilibrium state (where the methods are valid)
at the moment of explosion. All the analytical solutions for such a phenomenon can
be made only with a number of assumptions, which do make the final result just a
rough estimation.
Experimental study encounters even the worse hardships. It is impossible to
observe a Coulomb explosion in “real time”, because typical duration for such a
phenomenon is less than 1 ps, which is a bit of challenge even for the best of time-
846
Coulomb explosion and steadiness
resolve techniques; but even those methods cannot be used, since all the processes
always take place somewhere beneath the material surface. One may experimentally
observe an indirect evidence of Coulomb explosion only – the defects produced in
the depth of material and sputtered particles emitted by the surface in both. The
most successful way of observing is step-by-step slicing of investigated material with
further etching and electron microscopy, which is non-productive.
Coulomb explosion study in computer simulations gives at least better results
than “pure” analytical approach, because it permits to take into consideration a
non-linearity and other things which are hard to calculate analytically. A conventi-
onal method for Coulomb explosion study is the Molecular Dynamics (MD) method,
which is based on classical approach to atom movements in given potentials. This
is quite correct approach if the potentials are established correctly. It will provide
almost accurate results, if inter-atomic interactions are calculated using their wave-
functions (Car-Parinello approach). A time-dependent simulation of Molecular Dy-
namics permits to study the physical and chemical properties changeability with
time, which makes it convenient to understand. This method is non-contradictive
and the results can be verified experimentally.
The MD method was chosen as the basic for evaluations in the current work, as
the most promising and giving the most detailed representation of processes taken
place.
2. High-radioactive glasses as the object for simulation
Until now all the known manifestations of Coulomb explosion have been observed
mainly on the surface of various materials under the action of external short high-
energy pulses and particle bombardment. Meanwhile, there are materials containing
radioactive atoms dissolved in their volume, where the Coulomb explosion may occur
if their properties (charge relaxation time, ionization energy) are suitable.
LFCM (Lava-like Fuel-Containing Materials) are the materials formed as a re-
sult of well-known heavy nuclear accident occurred at Chornobyl NPP facility in
1986. As it is accepted now [7], the LFCM are glass ceramic alkaline-earth silicate
compositions (devitrified glasses) containing 5–10 mass percent of irradiated urani-
um nuclear fuel in their volume accompanied by high-radioactive fission products.
Quite up-to-date review of the main LFCM physical properties is represented in
[7]. Approximately 1,000 tons of this material, accompanied by both the other core
debris and the building constructions of the destroyed Chornobyl NPP 4-th unit,
is located in the so-called “Shelter” facility, which had been erected quickly after
1986 accident as a forced measure directed on primary prevention of radioactive sub-
stance dissemination in the environment. The “Shelter” facility is not a hermetically
sealed construction and there are no doubts that a large quantity of high-radioactive
compositions, such as LFCM and irradiated nuclear fuel itself do have a direct air
contact with the environment. LFCM themselves look like the coloured glass ceram-
ics and one can classify them like brown (8–10% fuel content) and black (4% fuel as
usually).
847
V.Zhydkov
Recent experimental research indicates, that LFCM are disordered semiconduc-
tors having energy gap width about 1.5 eV and Fermi level lieing 0.75 eV below
the mobility edge of conductivity band. These results were obtained mainly from
the measurements of LFCM electric conductivity on temperature dependence [8].
An ionic conductivity in LFCM turned out to be suppressed by Ca2+ and Mg2+ ion
presence and the electric transport in them provided mainly by electrons.
A LFCM specific radioactivity corresponds to the fuel content, but there are
slight deviations in isotopic proportions: due to some distinguishing features of lava
formation [9], LFCM as a whole turned out both to be depleted twice or more by
volatile fission products, such as Cs–137, and correspondingly enriched with some
transuranium daughter products (Pu+Am) in comparison with an irradiated fuel of
a similar burnup. Thus, up-to-date LFCM specific activity is about 20 MBk/cm−3
(α- activity) and can achieve 1 GBk/cm−3 (β-emitters, mainly Sr–90). Total estimat-
ed absorbed radiation dose in LFCM volume achieves of the order of 10 MGy up to
the moment, which is a significant level for dielectrics, where the energy dissipation
mechanisms through free electrons are negligible.
Another important property in LFCM physical behaviour is self-sputtering of
their surface. In the recent years a very interesting experimental fact was discovered
[10] – both the LFCM and irradiated uranium fuel surface have one remarkable
property: spontaneous dust generation capability, which means the capability of
a surface, without any external impact, to generate and disseminate into the sur-
rounding media the high-disperse phase (with the size of the particles mainly below
1µm), which in technical practice should be named as a submicronic dust. Such a
phenomenon had been preliminary investigated in workbench experiments, both by
providing smear tests [10] and by collecting the dust on special collectors in a high
vacuum condition. Recently the spontaneous dust emission phenomenon has been
independently detected in workbench experiments in Karlsruhe [11] where it was
identified as the emission of submicronic dust particles from recrystallized UO2 fuel
of a high burnup.
A certain possible physical mechanisms to be responsible for the above phe-
nomenon are unclear yet. No doubt, however, that particle emission from the surface
means the displacement of surface atoms (clusters) and should originate from the
processes quite similar to those leading to radiation damages. In [22] the possible
physical mechanisms for the observed phenomenon were under discussion, but the
giant sputtering yield, detected in experiment, was left out the satisfactory expla-
nation.
3. The way for molecular dynamics simulation
The first step for any simulation is elaboration of input parameters and establishi-
ng the physical model. As it was noticed earlier, one of the most important things
for simulation by the molecular dynamics method is a potential choice. The cur-
rent choice was taken between L-J (Lennard-Jones) potential, and material-specific
potentials, namely BKS (van Beest-Kramer-van Santen), TTAM and three-body
848
Coulomb explosion and steadiness
VKRE potential.
L-J was the first potential chosen for the research [12], but later it turned out
that the potential isn’t good enough for simulation of condensed matter containing
various sorts of atoms. So, the L-J potential was rejected and it was decided to
choose more precise potentials. Silica is the base of LFCM, as it was noticed earlier,
so it was decided to apply silica-specific potentials: BKS [13], Tsuneyuki, Tsukada,
Aoki and Matui (TTAM) [14] and Vashista, Kalia, Rino, Ebbsjo(VKRE) [15]. BKS
and TTAM do have common view in exp–6 form:
ϕ (rij) =
qiqj
rij
+ Aije
−rijBij −
Cij
r6
ij
, (1)
where rij is the distance between interacting atoms, qi and qj are their effective
charges, and i,j – their numbers. HereAij, Bij, Cij are the specified potential con-
stants, which depend on the sort of interacting atoms. The constants for BKS and
TTAM [13,14] are listed in Appendix. Effective charges are supposed to be −1.2e
for O atoms and 2.4e for Si atoms as suggested by authors.
As one may notice, the BKS and TTAM potentials do have an unphysical prop-
erty of diverging to minus infinity at small inter-atomic distances. At high tempera-
tures or some other conditions, it is a possible situation in the model simulated when
an individual atom may achieve sufficient kinetic energy to overcome the potential
barrier and fuse with another atom. For this reason, the potentials were replaced with
a simple harmonic potential when atoms become closed within a range 0.12 nm(for
Si–O interaction) and 0.17 nm (for O–O interaction). The Si–Si interaction is not
considered here because for this case both potentials have coefficient at the diverging
component (1/r6) equal to zero.
The TTAM potential was developed for the accurate evaluation of properties
in a crystalline state [14]. Derived from ab-initio Hartree-Fock self-consistent-field
calculations, Tsuneyuki et al. have demonstrated that four of the known crystalline
polymorphs are stable under this potential. They have also used this potential to
show the α to β structural phase transition at 850 K [16]. Hemmati and Angell
have shown that the BKS potential is superior to the TTAM potential for certain
properties of amorphous silica [17]. However, we include the TTAM potential in our
study for comparison purposes.
The BKS potential is based on ab initio calculations and experimental data
[13]. The authors claimed this as an improvement over the TTAM potential and
compared several structural observations between them. The BKS potential has the
same functional form as the TTAM potential. The only important difference between
them is that for BKS potential the Si–Si interaction has no short-range component.
The VKRE potential contains an additional three-body component in order to
simulate bond stretching and bending effects.
ϕ =
N
∑
i<j
ϕ
(2)
ij +
N
∑
i<j<k
ϕ
(3)
ijk , (2)
849
V.Zhydkov
where ϕ
(2)
ij is two-body potential part, which includes a Coulomb interaction, re-
pulsion connected with finite dimensions of ions, and a charge-dipole interaction
originating from the large electronic polarizability of O atoms; and ϕ
(3)
ijk is a three-
body part that has the form
ϕ
(3)
ijk = Bijkf (rij, rjk)
(
cos (θijk) − cos
(
θijk
))
, (3)
where i,j,k are the atomic numbers. The Bijkconstants and formula for f(rij, rjk)
function and average bond angle θijk values are given in Appendix as well. By this
part of potential the “bend” strength is taken into account, based on the estimated
strength of bond interaction and average bond angle θ. A graphical comparison of
two-body parts of potentials is presented in figure 1.
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
-5
-4
-3
-2
-1
0
1
2
3
4
5
E
n
e
g
ry
(e
V
)
r[A]
SiOBKS
OOBKS
OOTTAM
SiOTTAM
SiSiTTAM
OOVKRE
SiOVKRE
SiSiVKRE
Figure 1. The potential energy identified for BKS, TTAM and VKRE potentials.
Only two-body part of VKRE potential is shown. Coulomb interaction is omitted.
In numerical experiments simulating a collision of amorphous silica structure
with separate Si and O atoms having a kinetic energy of 10, 20, and 50 eV, the BKS
potential has been identified as more stable and providing smaller energy divergence,
compared with TTAM and VKRE potential, and therefore was chosen as the most
appropriate for simulations, which include collisions. Further tests and [18] in both
allow a suggestion, that BKS potential is more suitable for simulation of amorphous
silica. Regarding the above properties, BKS potential seems the most appropriate
one for simulations of defect formation in silica within the current research.
Coulomb part of potentials was calculated taking into account a Debye screening.
The Debye-Huckel screened Coulomb potential was estimated using the expression
ϕ(r) =
qiqj
r
exp(−k0r). (4)
850
Coulomb explosion and steadiness
Here k0 is the decay parameter, which was calculated from the known relation
k0 =
√
ne2
ε0kBT
, (5)
where ε0 is a dielectric constant and kB is the Boltzmann constant. As far as the
free electron concentration n is less than1011cm−3 at a room temperature, as it
was estimated for LFCM [8], value is too low (below 3·105m−1) to provide effective
screening at scales, where Coulomb explosion takes place (nanometers), but it was
taken into account for the sake of precision. For the cluster of positively charged
atoms, which is formed at alpha-particle flight, the screening effect was excluded,
because effective Debye screening is impossible in the area where there is a lack of
electrons.
4. Calculation for the charge density threshold
As it will be shown below, the energy linear density to be sufficient for Coulomb
explosion for alpha-particle is about 300 eV/nm. Such an energy loss rate corre-
sponds to the energy of alpha-particle of 0.5–1.2 MeV [19]. The energy losses for
energies higher than 1.2 MeV is lower because of weak interaction of particle with
media, and for energies less than 0.5 MeV the energy losses are also lower due to
low alpha-particle energy. Linear energy losses function for alpha-particle was de-
termined from the reference table for free path of alpha-particles in various media
[19]. Then the ionization threshold for LFCM, regarding the existing data [8], was
suggested as 1 eV without any exaggeration. Cascade of secondary electrons from
the particle collisions was suggested to be insufficient, because at ionization energy
of 1 eV the major part of alpha-particle energy dissipates into a direct ionization
process.
Finally, the charge distribution was calculated by simulation of a direct ioniza-
tion process and checked for correctness under assumption, that total electrostatic
potential energy increase should be equal to the energy losses. The last suggestion
seems to be realistic, due to the system being adiabatic. The calculated threshold
for local density of ionized atoms is about 50 nm−3 at the track center, which cor-
responds to the linear energy losses of 300 eV/nm. The estimated ionization track
width is about 1.8 nm.
5. The simulation procedure
The next important point after setting the type of potential and initial condi-
tions is choosing the correct equations of motion in order to calculate the atom
positions from forces with time. Theoretically, the most correct one for general pur-
poses of molecular dynamics is Gear’s predictor-corrector algorithm [20]. It turned
out, however, that the corrections used in this algorithm produce additional errors
when simulating collisions and other rapid changes in the system. Further, the most
851
V.Zhydkov
correct results were obtained when using the lowest order of the Gear’s predictor-
corrector algorithm. That is why the decision was to reject the Gear’s algorithm,
and use the Verlet integration algorithm with smaller timestep instead of it.
Simulation was set for a lattice of 9000 atoms with translational periodical con-
ditions for 2 nm in “depth” along the alpha-particle track and 8 nm in “width”
(perpendicular to the track). The system under simulation underwent an instant
heating to 7000 K, and then was quickly cooled in order to form an amorphous sili-
ca structure similar to LFCM. Some of the calculated parameters for the amorphous
structure are demonstrated in figure 2. After stabilization of the whole structure the
simulation of alpha-particle flight has been performed.
Figure 2. Radial distribution of distances between atoms in the material simu-
lated. Results for O and Si atoms for the amorphous silica are shown.
Then simulation was run by the established rules of molecular dynamics with a
timestep of 0.05 fs. During the simulation process the system was being constant-
ly checked for the energy conservation criteria and if the divergence turned out to
be too large (> 0.01%), the timestep was decreased. The total energy conservation
was also the crucial criteria to check the correctness of simulation process. Total
energy deviation starting from 0 fs and until 200 fs, when all the atomic displace-
ment had taken place, did not exceed the 10 eV quantity for the whole system,
which is a satisfactory accuracy in comparison with alpha-particle linear energy loss
(300 eV/nm).
The main results of simulation are represented in figures 3, 4.
In figure 3 one can see that majority of atomic displacements fall below the
0.2 nm range. Such small displacements cannot really be considered as “true” ones
for this case as far as they cannot provide the stable point defects due to amorphous
material structure and therefore cannot be classified as defects influencing on the
material properties. So, for the correct DPA calculations one should take into account
the only atoms being displaced on a distance more than size of crystalline silica
cell (near 0.38 nm). Those atoms only have been accounted as real displacements.
852
Coulomb explosion and steadiness
0.0 0.1 0.2 0.3 0.4 0.5
0
20
40
60
80
100
R
e
la
tiv
e
d
is
p
la
ce
m
e
n
t
fr
e
q
u
e
n
cy
Displacement distance, nm
Figure 3. Atomic displacements on range distribution as the result of Coulomb
explosion.
Figure 4. Distribution of kinetic and potential energy in material in the chosen
moments of time after alpha-particle flight. Left picture is the kinetic energy,
right is the potential energy and bottom is time passed after alpha-particle flight.
The alpha-particle flight direction is perpendicular to a picture surface. Energy
value corresponds to levels of gray, as shown on the scale by the left.
853
V.Zhydkov
The Coulomb explosion has practically 100% chance to occur, when the particle
linear (ionization) energy losses will exceed 300 eV/nm values. If energy losses will
be 100÷300 eV/nm, the Coulomb explosion still has significant chances to occur,
but its total power will be of one order smaller.
If to calculate DPA in the above way, it will result in about 40000÷80000 dis-
placements per each alpha-particle track depending on variations in material struc-
ture. This quantity is much more, than radiation damage quantity produced by
direct collisions of alpha-particle with atoms (300) and the ones produced by heavy
recoil nuclei (3000) [21]. The exact parameters for the radiation steadiness of LFCM
are unknown yet, but Coulomb explosion accounting in estimated radiation damages
quantity will no doubt have the significant influence on LFCM behavior prognosis
with time. The total estimated radiation damage quantities in LFCM regarding the
Coulomb explosion phenomenon are listed in the table 1.
Table 1. Estimated accumulation of radiation damages in LFCM with time.
Calendar year α−decay quantity per
cm3
Radiation damages
quantity, DPA
1990 0.4·1016 0.005
2005 1.45·1016 0.020
2015 2.2·1016 0.029
2050 4.6·1016 0.060
Additionally, each alpha-particle flight will be accompanied by 100000÷200000
broken silicate cycles (where Si bound with 3 oxygen atoms only) at 100 fs from the
moment of explosion, which may turn LFCM into molecular-pinhole porous system.
That is the additional factor for LFCM structure degradation, allowing oxygen from
air and water to penetrate into LFCM volume.
Naturally, the Coulomb explosion phenomenon does not exclude the existence
of “thermal spike” phenomena [23], because all the kinetic energy from Coulomb
explosion will finally be converted into a thermal (macroscopic) energy and can
form the “thermal spike” following just after Coulomb explosion and providing an
additional input in radiation damages.
Figure 4 illustrates the spatial distribution of kinetic and potential energy with
time. We can see multiple atoms in area of alpha-particle track gain high potential
energy, which is rapidly transformed into kinetic energy (extremely high effective
temperature), which rapidly diffuse and dissipate their energy in surrounding media,
transforming it into the “thermal spike”.
6. The practical outcomes
The results obtained here are the basis for further radiation damages quantity
calculations in silicate glasses having low ionization potential. These results may
854
Coulomb explosion and steadiness
provide the satisfactory explanation for high-radioactive dielectrics self-sputtering
[10–12] phenomenon. In [22] the possible mechanisms of self-sputtering were under
discussion. General explanation for observable giant sputtering yield was based on
considerations about electron sputtering [22], where numerous electronic excitations
may stimulate atomic displacements. It was not clear, however, in what namely way
the low-energy electronic excitations can lead to atomic displacements, which needs
much higher energy being beyond a certain threshold (16 eV for crystalline SiO2).
The Coulomb explosion phenomenon seems to be the namely physical mechanism
for such an energy transfer. It is not difficult to predict that Coulomb explosion
intensity will be enlarged greatly, if we apply an external electric field to the whole
system; regarding a high electric field occurring in the near-surface layer of radioac-
tive dielectrics, one can suggest that the near-surface Coulomb explosion should be
the main mechanism responsible for self-sputtering phenomena. That case, however,
is more difficult for quantitative modelling as well as to be the subject for further
research.
Another very important result is the established correlation (for dielectrics) be-
tween the electron ionization energy and their potential radiation steadiness. The
latter is of doubtless importance in creating a scientifically based forecast of LFCM
behaviour.
As far as LFCM belongs to a class of silicate glasses containing dissolved ra-
dioactive substances, the result may be universal for similar silicate matrices initial-
ly appointed for α-radioactive materials immobilization in technologies where the
vitrification of solid radioactive waste is under suggestion.
855
V.Zhydkov
Appendix
BKS and TTAM potential parameters
Table 2. Parameters for the exp–6 silica pair potentials. A is in eV, B is in Å−1,
and C is in ·eV·Å6.
Parameter BKS TTAM
AOO 1388.7730 1746.70
BOO 2.76 2.84091
COO 175.0 214.91
ASiO 18003.7572 10096.06
BSiO 4.87318 4.784689
CSiO 133.5381 70.81
ASiSi 0.0 5.95184 · 108
BSiSi 0.0 15.1515
CSiSi 0.0 0.0
VKRE potential parameters
Table 3. Parameters for the 3-body interaction for SiO2 glass from Vashista et al.
Aij rs1(nm) rs4(nm) rc(nm) l(nm) rc3(nm)
0.7752 0.443 0.25 0.55 0.1 0.26
σ i(nm) Zi(e) α i(nm3)
Si 0.047 1.2 0
O 0.12 –0.6 0.0024
nij
Si–Si 11
Si–O 9
O–O 7
Bjik θ̄jik
Si–O–Si 19.97 141.0
O–Si–O 5.0 109.47
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Кулонівський вибух та стійкість
високорадіоактивних силікатних стекол
В.О.Жидков
Інститут Проблем Безпеки АЕС НАН України
Отримано 16 серпня 2004 р., в остаточному вигляді –
20 серпня 2004 р.
Ця робота присвячена теоретичному вивченню кулонівського вибу-
ху в силікатних стеклах, що мають низький потенціал іонізації та
перебувають під дією внутрішнього альфа-опромінення.
Це явище було вивчено за допомогою комп’ютерного моделювання,
а саме методом молекулярної динаміки (МД); параметри так званих
лавоподібних паливомісних матеріалів (ЛПВМ), зважаючи на їх
практичну значущість, були вибрані за вхідні параметри для цієї
моделі.
ЛПВМ – високорадіоактивні стекла, які утворилися впродовж актив-
ної стадії добре відомої важкої ядерної аварії, що відбулася на Чор-
нобильській АЕС в 1986.
Комп’ютерне моделювання виявило, що кулонівський вибух дійсно
може мати місце в ЛПВМ і призводить до додаткових радіацій-
них ушкоджень під дією внутрішнього альфа-опромінення. Загаль-
на кількість атомних зміщень, утворених шляхом кулонівського ви-
буху від однієї альфа-частки, складає 40000 ÷ 80000, що більше за
радіаційні пошкодження від альфа-частки і важкого ядра віддачі,
взяті разом (близько 3500) більше, ніж на порядок.
Ключові слова: Кулонівський вибух, молекулярна динаміка,
радіоактивні стекла
PACS: 34.50.Fa, 34.90.+q, 72.90.+y
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